Geodesic
On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n
Fractional calculus and applied analysis, Tome 8 (2005) no. 4, pp. 393-401.

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There is given a generalization of the Marchaud formula for one-dimensional fractional derivatives on an interval (a, b), −∞ a b ≤ ∞, to the multidimensional case of functions defined on a region in R^n
Keywords: Hypersingular Integrals, Fractional Laplacian, Marchaud Fractional Derivative, 26A33, 42B20 
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Rafeiro, Humberto; Samko, Stefan. On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n. Fractional calculus and applied analysis, Tome 8 (2005) no. 4, pp. 393-401. http://geodesic.mathdoc.fr/item/FCAA_2005_8_4_a3/